BIT Numerical Mathematics

, Volume 32, Issue 4, pp 620–633 | Cite as

A-stability of Runge-Kutta methods for systems with additive noise

  • Diego Bricio Hernandez
  • Renato Spigler
Part II Numerical Mathematics


Numerical stability of both explicit and implicit Runge-Kutta methods for solving ordinary differential equations with an additive noise term is studied. The concept of numerical stability of deterministic schemes is extended to the stochastic case, and a stochastic analogue of Dahlquist'sA-stability is proposed. It is shown that the discretization of the drift term alone controls theA-stability of the whole scheme. The quantitative effect of implicitness uponA-stability is also investigated, and stability regions are given for a family of implicit Runge-Kutta methods with optimal order of convergence.

1980 AMS Subject Classification

65L20 (primary) 60H10,34F05 65L07 93E15 

Keywords and phrases

Numerical stability Runge-Kutta methods implicit methods stochastic differential equations stochastic stability 


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Copyright information

© BIT Foundations 1992

Authors and Affiliations

  • Diego Bricio Hernandez
    • 1
    • 2
  • Renato Spigler
    • 1
    • 2
  1. 1.CIMATGuanajuato, Gto.Mexico
  2. 2.DMMMSA, Università di PadovaPadovaItaly

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